Question

An 8-sided die is formed when two square pyramids are attached by their bases. The perimeter of the base shape is 6 centimeters. The distance between the tallest points of the two pyramids is 2 centimeters. What is the surface area of the 8-sided figure?

Answer 1

Consider one pyramid
Side length of base = 1.5cm and its height is 1 cm
Slant height of one of the lateral faces =  sqrt(1^2 + 0.75^2) =  1.25 cm
Area of one of the triangular faces = 0.5 * 1.5* 1.25 =  0.9375 cm^2

There are 8  of these so the required surface area = 8 * 0.9375 
=  7.5 cm^2 Answer

Answer 2

Answer:

The surface area of the 8-sided figure is 7.5 cm²

Step-by-step explanation:

The perimeter of the base of each square pyramid is 6 centimeters.

So, each side length of the base  $=\frac{6}{4}= 1.5\ cm.$

Two pyramids are attached by their bases and the distance between the tallest points of the two pyramids is 2 centimeters.

So, the height of each pyramid = 1 centimeter.

Now, lateral surface area of each pyramid

$=2a\sqrt{\frac{a^2}{4}+h^2}$

$=2(1.5)\sqrt{\frac{(1.5)^2}{4}+(1)^2}\\ \\ =3\sqrt{\frac{2.25}{4}+1}\\ \\ =3\sqrt{1.5625}\\ \\ =3(1.25)=3.75\ cm^2$

So, the total lateral surface area of two pyramids  $=2(3.75)=7.5\ cm^2$

Hence, the surface area of the 8-sided figure is 7.5 cm²